# Lean Angle == Turn Radius?

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Saying this detail and that are not predominant or marginal is not answer. In effect, you are saying that you don't know why the front is turned in nor what it is doing there.

And I never claimed to be an expert or a rocket scientist either! I thought this forum was all about sharing ideas and thoughts on stuff. I can only offer some ideas from a practical point of view. If you want the mathematical forumula that explains this phenomenon, you'll have to wait for someone else to chime in..

Yes, I understand the concept of rake and trail. And with all due respect, I think you'd stand a better chance at getting the answers you seek in a physics forum rather than a bike forum. If we take one of the wheels out of the equation, then whatever answer you get to your question won't be related to cornering technique.

I thought your question was why the radius increases as speed increases, at a fixed lean angle? But now you're asking why the front wheel "knows" how much to turn in? Well I "believe" and "have faith in" that it has to do with the trail (correlated to rake angle).

There's a lot on the subject here: http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_geometry

I did not intend to insult you or your knowledge. In fact, you seem to have a good firm grasp of the forces involved and the "what" of the matter at hand (hence why I am interested in your ideas, viewpoint and perspective). And I am not asking for someone to "give me the answer". Quite the opposite, in fact.

One part of my immediate purpose this morning as I was running around getting ready for work and posting in a hurry each time I walked past the computer, was to re-clarify my question (yet again) as it seemed at the time that we were talking past each other and that I was failing to make a connection. I suppose part of that could be chalked up to the fact that we were cross-posting. Or perhaps the fact that we speak different native languages. Or perhaps that I was simply in too much of a hurry to take the time to read carefully.

Another part of my immediate purpose, based on my respect for your viewpoint, was to stimulate an interest on your part by acknowledging the fact that operating a motorcycle without knowledge is akin to operating one's life "on faith". It seems I may have hit a nerve there. If that makes you uncomfortable... good. I think it should. And that was the point.

Operating without the big picture, living in ignorance as it were, sure makes me feel uncomfortable and out of control. And I think that's generally a very good reason to pursue an issue to find the solutions to alleviate the source of my discomfort and fear and the potential for it to cause aberration in my operations. I can respect that you might prefer to answer the question: "How does that work?" by saying "It works just fine". Hopefully you can respect that that answer doesn't work for me.

In any case, my overall goal in this thread is working through this particular question without "cheating" by consulting a physics site or asking "daddy" for "the answer". And to share that process with others who are interested in doing the same thing. I suppose you could say it's our geeky idea of fun. If that doesn't interest you, please feel free to choose another thread.

If it does interest you, I am not looking for a mathematical formula. I couldn't care less about the math of it. (But I would be happy to see it if someone knows it.) Mostly, what I am interested in is sharing my ideas and thought processes with others and reading about others ideas and thought processes and seeing how they fit together. Or don't fit together. Sort of like picking different pieces of a puzzle and seing what fits. And, so far, I think we have made great progress. And I'm having great fun.

Cheers,

racer

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At a given lean angle, the radius will change as a function of speed BECAUSE the front wheel is turned more inwards the slower you go (and less inwards the faster you go).

Today I'm leaning more toward the front wheel turning in (more and less) because the radius the bike (and rear wheel) is rolling is changing. In other words, the front wheel is always "trailing". At faster speeds, the rear is trying to come around or pivot around the front, hence, the angle the front is turned in would decrease as speed increases.

To me, this seems to fit with what Keith is saying in "Steering for the Rear", ie. the rear wheel is what stabilizes the bike and dictates the lean angle. I am thinking that the front will track whatever way the bike is going once it is leaned in.

And I am starting to agree with Carl that whereverf the weight is is where the control is. If you roll off the gas, now the front has more effect or control. If you are on the gas, the weight moves rearward and the front is more or less along for the ride.

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I have a question...if more speed causes the bike to run a wider radius at a given lean-angle, why is that when you get on the gas after flicking the bike over, the bike doesn't start drifting wide?

If I remember right, CSS teaches that chopping the throttle and/or grabbing the brakes will make the bike run wide and that more gas will make it hold its line. If you say that more speed increases turning radius, then why would the bike run WIDE when slowing DOWN and keep a CONSTANT RADIUS when accelerating? There have to be other forces at work, right?

Maybe I'm just confused, but no one's ever really explained the physics of it to my satisfaction...rake, trail, precession, torque-steer, gravity vs. centrifugal force...it seems like everyone has their theories and the "solution" is somewhere in the middle, or a combination of all of these.

Good questions, squirrels. Sorry I'm late for my pillow. I will sleep on it and try to reply in the AM.

G'night!

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If we take one of the wheels out of the equation, then whatever answer you get to your question won't be related to cornering technique.

Well, I guess I am not really after "cornering technigue" so much as mechanics. And breaking it down into components or sub-systems is a tried and true effetive method to get at that.

I thought your question was why the radius increases as speed increases, at a fixed lean angle? But now you're asking why the front wheel "knows" how much to turn in? Well I "believe" and "have faith in" that it has to do with the trail (correlated to rake angle).

I "believe" the questions are related. And that one inevitably leads to the other.

Well, if it has to do with trail corellated to rake, then I fail to see how ...

At a given lean angle, the radius will change as a function of speed BECAUSE the front wheel is turned more inwards the slower you go (and less inwards the faster you go).

These concepts seem mutually exclusive to me. It has to be one or the other. I don't see how it can be both.

But I do see how you can reach both with independent lines of reasoning... which is exactly what I have done as well!

Welcome to my asylum!!!

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Hmmm, I'm just thinking "out loud" here, so bare with me:

A "free" bicycle wheel (not attached to anything) going straight forward at 100mph is not likely to initiate any steering, turning or leaning on it's own. Because of the gyro effect, right..?

But once it has slowed down to 10mph, it'll probably start to "wobble" or swerve a little back and forth. So why is it swerving from side to side, rather than just falling down? It looks like there is some force or mechanism that helps "fighting back" the force of gravity, by continously correcting the steering angle to keep the CG from being pulled down to either side of the wheel. The round tyre profile means that the wheel radius is smaller at the edges than in the middle. So when the wheel dips in a little, the tyre will have to rotate faster due to the reduced wheel radius. What happens when the wheel starts rotating faster as it dips into the turn? The gyroscopic force increases, but what else? The lean angle causes the sentripetal force to kick in a little bit.. Anything else? I have a feeling that I'm missing something here..?

A wheel that's standing still will fall down as soon as you let go of it. A wheel that's spinning at 10mph is able to keep rolling all day, in theory. So what is the main difference between the two scenarios (standing still vs. moving at 10mph), what has changed? Well the obvious difference is the presense of gyroscopic (or centrifugal) forces. Are there any other differences, any other mechanisms that helps stabilizing and/or steering the wheel?

Another interesting thing to look at, is when the wheel eventually slows down to the point where it starts to go in circles. The radius tightens as speed decreases, until the tyre finally falls down. Again, I think there is a direct relation between speed, radius and lean angle (but WHYYYYY?)

Here's the elaborated version of "my" theory:

As the velocity decreases, the gyroscopic (stabilizing) forces become weaker and weaker, the gravity becomes "stronger" due to the increased leverage as the wheel leans more and more (trying to pull the CG down), and the sentripetal forces becomes stronger (trying to push the CG out).. And the reason why the tyre manages to "balance" it's lean angle to accomodate for it's speed is because of the law of physics that says: The sum of all forces are equal (at all times)

Am I getting closer? Here's a sketch I made to illustrate my point:

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I did not intend to insult you or your knowledge. In fact, you seem to have a good firm grasp of the forces involved and the "what" of the matter at hand (hence why I am interested in your ideas, viewpoint and perspective). And I am not asking for someone to "give me the answer". Quite the opposite, in fact.

One part of my immediate purpose this morning as I was running around getting ready for work and posting in a hurry each time I walked past the computer, was to re-clarify my question (yet again) as it seemed at the time that we were talking past each other and that I was failing to make a connection. I suppose part of that could be chalked up to the fact that we were cross-posting. Or perhaps the fact that we speak different native languages. Or perhaps that I was simply in too much of a hurry to take the time to read carefully.

Another part of my immediate purpose, based on my respect for your viewpoint, was to stimulate an interest on your part by acknowledging the fact that operating a motorcycle without knowledge is akin to operating one's life "on faith". It seems I may have hit a nerve there. If that makes you uncomfortable... good. I think it should. And that was the point.

You're a standup guy, racer. I accept your "pardons" and your explainations

You had me going for a while there, though. I was starting to get the wrong perception of you, the way you "killed" my thoughts on the subject..

Oh well, I respect your quest for knowledge, and now that I've "figured you out", I won't take it personally when you critisize my ideas.

..and I see how the language barrier might have caused some extra mess too.

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I thought your question was why the radius increases as speed increases, at a fixed lean angle? But now you're asking why the front wheel "knows" how much to turn in? Well I "believe" and "have faith in" that it has to do with the trail (correlated to rake angle).

I "believe" the questions are related. And that one inevitably leads to the other.

Well, if it has to do with trail corellated to rake, then I fail to see how ...

At a given lean angle, the radius will change as a function of speed BECAUSE the front wheel is turned more inwards the slower you go (and less inwards the faster you go).

These concepts seem mutually exclusive to me. It has to be one or the other. I don't see how it can be both.

I can see why these concepts seem to be mutually exclusive, but I still think they are describing the same thing. I'll try to use both concepts in a single scenario:

As you're cruising down the straight highway, you can let go of the handlebars and the bike will keep going in a straight line due to trail. The more trail, the more the bike want's to go straight forward. So on a Harley with stretched forks, you have to push harder to make the bike turn. By exaggerating this example, it becomes easier to understand why. Say the forks were 20 feet long. That would give an extreme rake angle (more than 45 degrees), causing the front wheel to steer more on the X axis (horizontally) than on the Y axis (vertically). We can easily imagine how difficult it would be to negotiate a sharp corner with such a freaky steering geometry. And the steeper the rake angle (like on a R6) the more "turnable" it gets at the cost of stability. This isn't really a good explaination, it's more of an observation. But at least it proves and establishes that the trail plays an important role when steering the bike.

The second concept (radius changes as a function of speed beacuse the front wheel is turned inwards less (=larger radius) the faster you go) still holds true in my opinion. If you ride in a straight line and climb over to one side of the bike, the bike will lean over to the opposite side in order to balance CG. But alltough the bike is leaned over, maybe as much as 20 degrees from vertical, the bike will still go straight forward unless you give steering inputs onto the handlebars. So Lean Angle by itself does thereby NOT equal to radius, which tweek also found out on his latest CSS course. I'll go out on a limb here, and suggest that "Steering angle (not lean angle) = Turn radius". This applies as long as both wheels have good traction. One can't negotiate a turn using the same lean angle at both 10mph and 100mph, and no one will object to that. And thanks to the ingenious design of the positive rake angle (trail), the bike corrects itself, balancing all forces (lateral, vertical, sentripetal, you name it) to accomodate for speed and front wheel turn-in.

I know, I still haven't been able to break these concepts into smaller factors, analyzing exactely what's going on. As you (racer) said, I'm the kind of guy who figures out HOW stuff works (and I'm happy with that), while you also want to know WHY stuff works the way it does. I'm afraid I can't get any further as to explaining WHY on this subject..

But I could ask my dad if you ever give up, he has the answer to everything related to physics

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Just a few quick thoughts.

Centripetal force is the force that is exerting it's influence/push TO THE INSIDE (center) of the turn. That's created through steering into the turnwith the front wheel AND conical turning influence of a leaned tire. Centrifugal force (to the outside) is a "felt" effect, not a force. It is what a person feels in a turn pressing them to the outside so it's given a name. HOWEVER that is the result of forward momentum trying to go straight WHILE centripetal force tries to push things to the inside creating a turn. The Centrifugal force is the felt combination of trying to go continue going straight and trying to turn inward at the same time. IT can be FORGOTTEN when thinking about a bike in a turn. It is instead the momentum forward speed, and inward centripetal force that must balance equally against gravity for a bike to have a constant lean and turn.

To balance gravity, if the speed is low (force small), the inward turning centripetal force will have to be higher to add up to enough for balancing gravity. If the speed is higher (high force), the inward turning centripetal force will have to be correspondingly lower to balance the same gravity (same lean angle).

A bike can have any amounts and combinations of forces going on that do not balance but it will be unstable then and left that way long enough without change, heading for a crash. That's how we initiate a turn, destabilize it to tip in, and re-stabilize it again in a leaning/turning attitude. There has to be that balance of forces for it to be stable in a turn where it carves a constant radius.

Change any one thing and the others will have to do a corresponding change or stability will be gone. Stability is gone tipping in and straightening back up. Stability happens mid turn where you follow a constant radius.

Decrease speed and you will have to change lean angle, and or turn in (centripital force=radius) to get balanced status quo again. (hard thing is that when you steer you have both countersteering (changing lean angle) AND the front going in the direction the wheel is pointed, with the rear following it, happening AT THE SAME TIME.

Decrease radius (turn in, centripetal force) and your lean angle or speed will have to change.

Decrease lean angle and your speed and or radius will have to change.

That's in order for a balanced constant state to be achieved that is.

You can't single things out much because EVERYTHING here is having it's input at the same time and has it's influence on balance of forces. It's all interrelated, change one thing and everything in the whole system has to also change to get balance again.

Trail, happily when you lean the bike the contact patch moves inward causing the trail to steer the front wheel into the lean some (what turns out to be actually needed). Also the wheel tries to point in the direction the headstock/forks/axle are moving in. That's due to it's trailing along behind the rake of the forks/headstock angle.

If I take my heavy two up bike out (Bandit) and run cones at slow speeds with it in a parking lot, the front IS NOT trailing along enough for the tight turns to be made with little steering input. I have to physically help turn the front wheel into the lean enough to make the tight turn. It turns in on it's own yes, but is too slow about it and the bike would fall over before the trail could catch up and turn the front inward enough.

The rear wheel follows the front and the bike makes the tight radius. I then "over turn" the front wheel into the turn (turn too sharp), that countersteers the bike (front wheel turns in and axle moves to the inside faster than the headstock can follow), the bike stands up out of the lean, I "hold" the turn in (the trail does not do it) and the bike stands up straight and leans in the other direction (for a turn in the opposite direction now) as the wheel continues to move faster than the headstock can follow (the top of the bike cannot keep up with the bottom front wheel causing lean). At this point the trail tries to turn the wheel into the new turn in the other direction (doing cone weaves). HOWEVER, I need to hurry it up on that bike (help it). It is not a passive does it's own thing system at that slow speed. It tries but is heavy and slow about it. The bike feels heavy steering because I have to do a lot of steering myself with it at that particular slow speed maneuver. If I was willing to do less tight turns, I could wait for the trail and manage speed properly to not have to add my steering input I would think.

My point being, the front does not always just trail along. Even when it does it is still doing a sizable portion of creating centripetal (radius following) force, WHILE it also can potentially be countersteering as well AT THE SAME TIME.

If the front is turned in too much or too little to help speed balance gravity, THEN the bike undergoes countersteering. That's an important point.

Even when the bike is countersteering, the whole machine does try and follow the direction of the front wheel. That's another important point.

Countersteering happens when the top of the bike can't quite keep up with the bottom front wheel as it rolls out from under the bike to one side or another. When the bottom front wheel of the bike goes farther right than the top of the bike does, the bike leans more left. You could steer the wheel left then and steer so sharply it rolls the front back under the bike and straightens it up again. Both of those things are countersteering and the rider is the one who initiates it, leaning the bike into a turn and standing the bike back up coming out of a turn. The front axle and lower front part of the bike still ALWAYS follow the direction the front wheel is rolling. The difference is in what the top of the bike does, whether it follows along or not. In the balanced mid portion of the turn the top of the bike is following the front wheel along with the axle and the bottom of the bike AND the rear wheel is being brought along. That's so long as the front has some weight and traction.This is during mid turn status quo.

I do maintain that weighting one wheel over the other correspondingly increases the influence of the weighted wheel. Hence you can have the hinged headstock influencing more, or the unhinged swing-arm stabilizing things more. Have someone sit on a bike and you kick the front wheel sideways. Then go kick the rear wheel sideways. The front will destabilize with ease causing the forks to turn. The rear just receives a bump from the same force kick. It's all because of the direction of the steering hinge.

By the way, conical steering does work as you can lift the front end of a bike off the ground mid turn in a wheelie and continue to turn on the back wheel. You are however stuck with the singular radius that conical steering produces and so speed and lean have to be correct for it to work (as the front can no longer help by changing radius through steering or lean through countersteering). In a tight turn where the front wheel is needed to get the desired radius the turn would open up when you lifted the front off the ground. This follows in the real world.

I maintain the conical turning of the leaned tire AND THE AMOUNT you or the trail steers the front into the turn creates the centripetal force that combines with speed to balance the falling gravity force of the lean. If you or the trail don't turn in enough for the speed there is no balance. If you or the trail turns in too much there is no balance. The amount of turn in needed depends on lean angle and speed.

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Just a few quick thoughts.

...

That was a lot more than a few quick thoughts, dude!

I don't know what to say other than that YOU'RE GOOD! Everything you said makes perfect sence to me. There were actually no big surprises in there, but you managed to tell the whole (rather complicated) story in a very precice and understandable way. I now have a better picture of how everything is connected. BTW, you're also absolutely right, I mixed up sentripetal and sentrifugal forces. (Sorry if I mislead you, racer)

Centripetal force = radius --> Thanks for clearing THAT bugger up once and for all!

My hat goes off for you, great post!

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Amen!

Thanks leftlaner, I hope I am correct, which i think I am.

Here's a quote from a guy currently on a trip to and around Alaska that I think relates to this thread and the need for a balance of forces.

"Dempster Hgihway has changed a lot since I was up here in '99. It is much wider in most areas, but the wind on the ridge of the Ogilvie Mountains is still just as strong. Think about leaning against a strong wind from the right and still leaning right when you turn to the left!!!"

this also helps prove in my mind that you can steer the front wheel of the cycle in a direction and the rear and indeed the whole cycle will follow so long as gravity is balanced out correctly with any forces involved. the wind was in part the centripetal force in this case. He was leaning right and still able to countersteer, then steer left and turn left while leaning right into the wind. He was reducing the winds centripital (inward) force with lean angle (gravity) until the bike went straight, then he lessened the lean angle (gravity) pushing on the wind, so the centripital force would start moving the bike inward, and so the bike WOULD turn even though he was still leaning the wrong way. I'm saying the bike could not turn without the front whee being pointed into the turn some (the correct amount to balance out momentum, centripetal force, gravity to get the desired radius). In this ODD case wind AND wheel pointed in to desired radius was centripetal force.

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You're a standup guy, racer. I accept your "pardons" and your explainations

You had me going for a while there, though. I was starting to get the wrong perception of you, the way you "killed" my thoughts on the subject..

Oh well, I respect your quest for knowledge, and now that I've "figured you out", I won't take it personally when you critisize my ideas.

..and I see how the language barrier might have caused some extra mess too.

Thanks for understanding.

Be back soon.

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I have not had time to read through the last few posts entirely or well, but, a couple of things occured to me while skimming. (Leftlaner pretty well spelled out these ideas)

At nominal speeds, gyroscopic force will stabilize a wheel at whatever lean angle it is at. Expermiment with a bicycle wheel hung from a string and watch as it defies gravity and maintains whatever angle or position wrt gravity/earth that it is placed.

So, I believe that, properly, what might be being balanced between gravity and centrifugal force is all the rest of the non-rotating mass attached to the wheel.

So, IMO, while the front wheel is pointed into a corner, without pressure on the bars, just like going in a straight line, it is trailing. And, the angle of the front wheel is an effect of lean angle (due to rake/trail), not a cause.

Like carl alluded, there is a difference between steering in the sense of causing a change in direction (left right like a car) and steering in the sense of determining the direction in a stable state (or conical steering).

In the case of the bike being leaned into the wind, it will be countersteering. The front wheel is not neutral or trailing then. I believe that pressure is being applied to the bars to maintain the line. IN that case, once that pressure is released, the front wheel becomes an effect again. Not a cause.

Forgive me if this was acknowledged above somewhere, and for not responding directly to points made. I really am too tired to read through it all again tonight with any understanding. My head hurts too.

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OK... one last thing before I go to bed.

When the fork compresses, the wheel base is shortened, hence the wheels are closer together on the arc of the path they are traveling. But does the wheel angle (turned into the corner) change?

If the forks extend under acceleration, the wheelbase lengthens and the wheels are further apart on the arc. Does the turn angle of the wheel change?

Does the rake and trail change?

What happens to the line?

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PS -

leftlaner,

What software program did you use to create your beautiful graph/illustration?

I have had limited success creating that type of illustration and would really appreciate any hints or help.

Thanks,

racer

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I significantly edited my post above after leftlaner read it. (I saw you pop in and out)

I have not finalized my observations of whether the angle of the wheel changes due to cornering force or weight on the front regardless of wheelbase. I do think that its angle is determined mostly by rake and trail and may change at different lean angles as well. But just one lean angle for now.

2bigalow admitted that the hook turn is caused when the bike turns sharper due to a shorter wheelbase caused by weight compressing the forks.

So, if the wheelbase shortens with the same turn angle on the front wheel, the bike turns sharper. So, the angle of the front wheel seems to determine the arc or line the bike travels.

Carl said, way back (and i agreed), that he thought the amount of weight on the front wheel affects how much effect the front wheel has on the arc.

But, once the wheel is sufficently lightened, or even comes off the ground, does something change?

Of course for that to happen, there is acceleration happening.

OK, my head really hurts now and I am really going to bed this time.

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I significantly edited my post above after leftlaner read it. (I saw you pop in and out)

I have not finalized my observations of whether the angle of the wheel changes due to cornering force or weight on the front regardless of wheelbase. I do think that its angle is determined mostly by rake and trail and may change at different lean angles as well. But just one lean angle for now.

2bigalow admitted that the hook turn is caused when the bike turns sharper due to a shorter wheelbase caused by weight compressing the forks.

So, if the wheelbase shortens with the same turn angle on the front wheel, the bike turns sharper. So, the angle of the front wheel seems to determine the arc or line the bike travels.

Carl said, way back (and i agreed), that he thought the amount of weight on the front wheel affects how much effect the front wheel has on the arc.

But, once the wheel is sufficently lightened, or even comes off the ground, does something change?

Of course for that to happen, there is acceleration happening.

OK, my head really hurts now and I am really going to bed this time.

OK, a lot of questions at the same time here. I think that as long as the bike is balanced and stabile (carrying lean angle or not), then the front wheel is per definition "trailing". When the rider changes this situation by (counter)steering the bike is momentarily unbalanced. At this point I'd say the front wheel is "steering" more, and "trailing" less. By shifting the weight forward, this somehow affects the forces involved (sentrifugal, and gravity?) in a way that makes the front wheel "want to" stand up the bike in order to stay in balance. Someone with more knowledge should step in and explain this in detail..!

By shifting the weight rearwards, I guess the "conical steering" has a greater effect, and the front wheel trailing/steering becomes less significant, to the point where the front end lifts off and all you got is conical steering (which isn't quick and precice compared to front wheel steering).

PS. I used a very high-tech illustration program called "Paint", which is a modern version of the wellknown "Paintbrush"..

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PS. I used a very high-tech illustration program called "Paint", which is a modern version of the wellknown "Paintbrush"..

ha ha

MS Paint?

That's what I used to create my "stick figure" type drawing. I guess I just need to spend more time with it then.

Thanks.

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I dont log on for a week and I finally come back to this link thinking a couple of replies were posted. WOW!

That's alot of info.

I'm with sleepr, my head hurts. I bet this is what a round table at NASA sounds like when trying to figure a problem.

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I'm just going to pick on a couple of points.

I do know that when the front suspension compresses rake steepens and trail shortens along with the wheelbase. The front wheel takes on more of the load of the bike's weight as well (amount depending on whether the brakes are applied or throttle off or not). If the bike is accelerating and a bump compresses the forks the rake, trail, wheelbase shorten but the front wheel may not take on more weight and could even be in a state of lessening weight due to acceleration shifting the bikes CG rearward.

As to countersteering into the wind:

The rider has to push the bars, countersteering to cancel the centripetal force of the wind, thus progressively leaning the bike into the wind, UNTIL THE CORRECT amount of lean is found. That's where gravity (lean angle) balances the centripetal force of the wind. AT THAT POINT, when a balance of gravity against the other forces is established and the bike describes a constant path at a constant lean, there is no more countersteering happening. Lean angle is constant, path is constant since things are in balance. It doesn't matter that the rider has to maintain a certain pressure to keep the forces balanced (feeling like countersteering to the rider). It doesn't matter that the bikes trail and gyroscopic effects can't do that on their own, due to the added centripetal (sideways or inward) component of wind. What matters is the bike is in a state of relatively balanced forces and so is not countersteering anymore. Status quo is found regardless of riders need to press the handlebar to keep it. As soon as some input (steering, path direction change, change in wind's centripetal force etc), as soon as one of the forces involved change enough to disrupt balance of forces the bike is AGAIN countersteering until the new balance is achieved, or things degrade far enough for a crash.

So, if the forces of momentum, centripetal force, and gravity are in balance the bike is NOT countersteering. The lower portion of the bike is following the direction of the front wheel at the same rate as the axle. The top of the bike (headstock, tank, rider etc.) is on a parallel path to the bottom of the bike (axle lower frame etc.). That's true whether turning or going straight, whether pressing on the bar or not. It's true whether the bike's trail is keeping things in balance or the rider is doing it.

If the forces of momentum, centripetal force, and gravity are OUT of balance, THEN the bike is in a state of countersteering (a state of unbalance) . This is regardless of what the rider has to do pressure wise on the bars (regardless if it is the trail doing the deed or the rider doing the deed of balance or unbalance). I say unbalance of forces on the bike is countersteering because in unbalance, the top of the bike (headstock) is NOT exactly following the bottom of the bike thus creating a lean angle/gravity change. When the bike is countersteering it is in an unbalanced state where the bottom of the bike is on one path and the top of the bike is on a non parallel path thus changing lean (the bike is countersteering).

When the headstock does not exactly follow the direction of the axle's forward movement, lean angle changes (if the front axle and wheel moves to the right and the headstock lags behind moving right on a slower wider arc, then the bike leans left as an example). The front axle can be steered out from under the headstock, or back under it. This is done by pointing the front wheel in a new path. This is countersteering and reflects an unbalanced state of forces on the motorcycle.

When the forces of momentum, centripital force, and gravity balance, the headstock follows a parallel path to the front axle, both moving in a direction at the same rate, and the bike is in balance (whether going straight of describing an unchanging arc). At that point NO COUNTERSTEERING is happening, and the bike travels a straight line or a constant arc at a constant lean angle. SO, it can be said, if the headstock exactly follows the direction the front axle is traveling in on a parallel path, at exactly the same rate of travel, the bike is in a state of balance of directional forces and is in balance. If the headstock is on any slightly different non parallel path than what the front axle is moving in, the bike is in a state of countersteering because the lean angle and ultimately the path of the bike will be changing. The balance between momentum, centripetal force, and gravity will also be altering (in flux or inbalance ).

SO, balance of forces and constant path, there is no countersteering going on and everything top and bottom goes in the direction the front axle is moving (the direction the front tire is pointing) at a UNIFORM rate. Thats so even if the bike is leaning into the wind going straight, and the rider is pressing on the bars to keep the forces balanced.

In an unbalanced state of the forces mentioned, the top of the bike (headstock tank rider etc.) is moving in the direction the front axle is pointed at some different rate and different path over time. The bike is changing lean angle not keeping it constant.

Very important to getting a grasp on this is the fact that the axle and lower portion of the bike will ALWAYS HAVE TO follow the direction the front wheel is pointed, period (that is UNLESS the front tire is sliding or off the ground). It physically HAS to, things are bolted together and not made of rubber bands, and a rolling tire goes where it's pointed if it isn't sliding. Change where it's pointing, you change where the bottom of the bike is going. At a slower rate (due to momentum) you change where the top is going as well. The reason the bike's top can change direction of path slower than the bike's bottom, is the bike can lean, since there are two wheels not 4, and the top is not directly bolted to the wheel on a vertical plane like the front axle is.

The rear wheel is ultimately connected to the front wheel and HAS TO trail along in some manner (UNLESS it is sliding).

Now the rear under weight shift can INFLUENCE "the direction the front points" as the front directionally trails a balance of the forces acting on it. But, the direction the front is pointing matters much so long as it has traction.

I have to mention that in reality, the bike is only "moments" in an actual state of balance as it "hunts" back and forth for balance. It gets a tad out this way, mildly over corrects, gets a tad out the other way, and does a constant slow weave even when going straight. It's so small you don't feel it but it's always "hunting for balance" even when it feels stable. It confuses the issue talking about it though as it adds further complexity to a complex subject. So, best to ignore this small unbalance hunting effect when trying to think of balance/unbalance of the bike when turning. In reality the bike is always countersteering itself a tiny amount when acting stabilized. That just makes things harder to grasp though so I'm ignoring it for the most part. Though it may lead to clarity of thought in discussion of how trail is trailing along, and how the bike finds balance of forces from that.

The front trails along, and when you write that, it appears language wise, to imply it is passively following without exerting turning influence or force acting through it, that's not so though. When cornering, the forces of momentum, centripetal force, gravity, and forces due to trail are duking it out at that front contact patches well as at the rear. Beyond this I haven't thought through things with trail and trailing along yet. It seems to me the answer would lie in forces at the contact patch and how they balance or unbalance.

However think about it, if the bottom of the bike did not HAVE TO follow the direction the front wheel is pointed in, then the rear and front wheels conical steering would wholly determine radius alone, countersteering WOULD NOT work, and turning the front wheel into the turn full lock would have no effect. The fact that putting pressure on the bars one way or another DOES countersteer a bike, proves the bottom of the bike HAS to follow the direction the front wheel is pointed period. The front always has an influence on direction until it is off the ground.

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So, Carl, you're saying that my two main thesis were basicly correct?

1) When the bike is at balance, the bike will go where the front wheel is pointing. The main reason why the bike follows a larger corner radius at higher speed, is due to the fact that the front wheel is pointing less inward (which it has to in order to keep the rubber side down)

2) Lean angle is determined by the relation between velocity and radius. Radius is determined by the relation between velocity and lean angle. Velocity is determined by the relation between lean angle and radius. The three factors influence each other, so you can't take any of these factors out of the equation, or calculate one of these factors unless you know the other two factors.

So, the question is: Why does this sound so much smarter when Carl says it??

I'm starting to regret that I didn't take that physics class back at high school.. sigh (yes, my head hurts too!)

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So, Carl, you're saying that my two main thesis were basicly correct?

1) When the bike is at balance, the bike will go where the front wheel is pointing.

The BOTTOM of the bike will go where the front wheel is pointing always, regardless of whether the rider or the trail points it, unless it's not on the ground, or sliding. When it's in balance the top goes there too on a parallel path. However, the conical steering action of the front and back tires being leaned, will also be acting on radius. radius is the result of where the wheel is pointing AND the conical steering.

Traveling a path on a radius produces centripetal (inward) force.

The main reason why the bike follows a larger corner radius at higher speed, is due to the fact that the front wheel is pointing less inward (which it has to in order to keep the rubber side down)

Yes. If the front did not behave so, the bike would go into countersteering state instead of balanced status quo, and so eventually crash through the changing lean angle that unbalances the forces.

If you instantly turned the front wheel in at 50mph like you do at 10mph the bike would lose front traction, slide away and lowside. If it could maintain front traction it would high side. If you turned the front wheel only the amount it turns at 50mph, but were going 10mph, the bike would continue going into a steeper and steeper lean until it fell over lowsiding. the three main forces would be out of balance. The bike would be acting continually as it acts in countersteering, changing lean angle. it would do that until disaster unless the forces were changed to re-balance themselves.

2) Lean angle is determined by the relation between velocity and radius.
Since traveling a radius produces centripetal force, I guess yes. lean angle NEEDED for balanced status quo, is determined by velocity and radius. Actually any lean angle is determined by velocity and radius as well as direction of turning (left/right).

Radius is determined by the relation between velocity and lean angle.
Radius NEEDED to achieve balanced status quo is yes.

Velocity is determined by the relation between lean angle and radius.
the velocity NEEDED to maintain the other two at an unchanging level and get balanced status quo is yes.

The three factors influence each other, so you can't take any of these factors out of the equation, or calculate one of these factors unless you know the other two factors.
If you are looking for a balanced state of these forces in the bike, yes.

So, the question is: Why does this sound so much smarter when Carl says it??
Because I'm stuck with using WAY too many words to try and explain myself. That's not a good thing by the way.

I'm starting to regret that I didn't take that physics class back at high school.. sigh (yes, my head hurts too!)
Like I said before, I don't know from physics. I'm just trying to practically figure out the factors at play which are numerous and some of which haven't been addressed yet when it comes to the effects of trail and some other things I think. Such as, when you accelerate, the rear tries to pivot around the headstock/fork angle, where it contacts the ground when a line is drawn through the center of the forks top to bottom.

Slip angles will complicate things too I'd guess. How the contact patch behaves may complicate them as well.

Then again you have the chance that I am totally wrong :-D I just don't think I am yet.

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he he he

this is awesome stuff. exactly what i hoped for. thank you everybody for your time and effort ( and pain! )

unfortunately i am totally mentally blown out from yet another 12 hour day on 5-6 hours of sleep (wearing five different hats while learning yet another). i can't remember my last day off... at least 3 weeks ago. so, i am having difficulty using the shift key tonight much less reading through carl's posts. dude, you have to learn to use less words.... lol. (kidding! )) seriously, i really dig your posts, i just need more time to read them!

that said...

i think you/we/us have really nailed down the landscape wrt three basic inter-related variables. to quote lando molari, "I believe we have it surrounded!". really great stuff.

like so many things in analysis, perception depends on the node from which a system is analyzed (up looks like down from over there) and everything is dynamic and in flux hence attempting to nail down a single slice or moment in time with a static freeze frame snapshot can really make things more difficult to grasp, yet, at the same time, looking at all the angles, turning it this way and that, taking it apart and putting it back together from each direction can be really valuable.

considering our progress so far, I can see that I was trying to bite off too much at once. hopefullly, everyone is close to being on the same page now. (eyes bottle of headache pills warily)

ok, enough talking about talking. moving on...

i like the angle of saying that the front wheel must turn outward more to accomodate more velocity for the system to remain in balance. if that is true, then here is my question...

why is the front wheel turning out more at a higher velocity (without a higher rate of acceleration), what is causing that to happen? i don't mean what is the primary mover, i mean the mechanics of it. there is more centrifugal force that needs more centripetal force to balance it, (I believe the centripetal force is being supplied by the pavement and is essentially limited by the amount of available traction) i mean, where is the lever? is it simply more centripetal force applied orthogonally to the angle of the front wheel at the contact patch which is behind behind the steering stem angle due to the rake/trail (like 2big and i discussed way back when)? hence that forces the wheel to turn outward...

yes, that makes sense. that really makes sense. wow. I need to think through the other angles but i'm feeling excited.

so that might explain the front wheel angle... but... i still feel like the "conical steering" at the rear wheel has to dominate the system if the bike is accelerating, ie on the gas. the front must be trailing or it would countersteer the bike. it is like the inverse of countersteering as the the wheel turning outward actually maintains the lean angle... or does it? (or would prevent the bike from coming up from that lean angle). BUT the stabilizing gyro force at the rear is what really keeps that from happening... that keeps the bike from coming up. the front simply must turn outward due to increased centripetal force and the rake/trail. but is it really what causes the bike to run wide or is it a response to the bike running wider?

a gyro stabilized wheel will not come up with increased velocity. hence the rear wheel MUST run wide due to the gyro force.. and and and... here it is... holy ######.... it's the precessional forces that turn the rear outward due to the torque applied to the rear wheel itself!!!

whoa.

is that it? can that be it? it has to be. oh wow. i have to go sleep on this.

warning: stand clear.... epiphany in progress...

and if the front comes off the ground, the rear still runs wide!!!

HA!!! HAAAA!!!

I did it!!!

er... WE did it!!!! (heh heh)

hahahahahhaahhahahhahahahahahahahhhaah

(turns handsprings in his mind)

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ok, i have to sleep on this, but, i really think that's it.

two years ago when i studied gyroscopic precession, i came to the conclusion that leaning the bike in causes a turning in force at the rear wheel, but, I never thought to turn that around. wow.

i really think we did it. i'm totally stoked.

thanks everybody. thank you thank you thank you.

hehehehehehehehe

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and and and... here it is... holy ######.... it's the precessional forces that turn the rear outward due to the torque applied to the moment arm defined by the wheel itself!!!

Aaaahh!! Now I get it..! ....not

You totally lost me, dude. When you find the time, please explain this concept in English (layman's words)..

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